Ejemplo n.º 1
0
/** Executes the algorithm
 *
 */
void SplineBackground::exec()
{

  API::MatrixWorkspace_sptr inWS = getProperty("InputWorkspace");
  int spec = getProperty("WorkspaceIndex");

  if (spec > static_cast<int>(inWS->getNumberHistograms()))
    throw std::out_of_range("WorkspaceIndex is out of range.");

  const MantidVec& X = inWS->readX(spec);
  const MantidVec& Y = inWS->readY(spec);
  const MantidVec& E = inWS->readE(spec);
  const bool isHistogram = inWS->isHistogramData();

  const int ncoeffs = getProperty("NCoeff");
  const int k = 4; // order of the spline + 1 (cubic)
  const int nbreak = ncoeffs - (k - 2);

  if (nbreak <= 0)
    throw std::out_of_range("Too low NCoeff");

  gsl_bspline_workspace *bw;
  gsl_vector *B;

  gsl_vector *c, *w, *x, *y;
  gsl_matrix *Z, *cov;
  gsl_multifit_linear_workspace *mw;
  double chisq;

  int n = static_cast<int>(Y.size());
  bool isMasked = inWS->hasMaskedBins(spec);
  std::vector<int> masked(Y.size());
  if (isMasked)
  {
    for(API::MatrixWorkspace::MaskList::const_iterator it=inWS->maskedBins(spec).begin();it!=inWS->maskedBins(spec).end();++it)
      masked[it->first] = 1;
    n -= static_cast<int>(inWS->maskedBins(spec).size());
  }

  if (n < ncoeffs)
  {
    g_log.error("Too many basis functions (NCoeff)");
    throw std::out_of_range("Too many basis functions (NCoeff)");
  }

  /* allocate a cubic bspline workspace (k = 4) */
  bw = gsl_bspline_alloc(k, nbreak);
  B = gsl_vector_alloc(ncoeffs);

  x = gsl_vector_alloc(n);
  y = gsl_vector_alloc(n);
  Z = gsl_matrix_alloc(n, ncoeffs);
  c = gsl_vector_alloc(ncoeffs);
  w = gsl_vector_alloc(n);
  cov = gsl_matrix_alloc(ncoeffs, ncoeffs);
  mw = gsl_multifit_linear_alloc(n, ncoeffs);

  /* this is the data to be fitted */
  int j = 0;
  for (MantidVec::size_type i = 0; i < Y.size(); ++i)
  {
    if (isMasked && masked[i]) continue;
    gsl_vector_set(x, j, (isHistogram ? (0.5*(X[i]+X[i+1])) : X[i])); // Middle of the bins, if a histogram
    gsl_vector_set(y, j, Y[i]);
    gsl_vector_set(w, j, E[i]>0.?1./(E[i]*E[i]):0.);

    ++j;
  }

  if (n != j)
  {
    gsl_bspline_free(bw);
    gsl_vector_free(B);
    gsl_vector_free(x);
    gsl_vector_free(y);
    gsl_matrix_free(Z);
    gsl_vector_free(c);
    gsl_vector_free(w);
    gsl_matrix_free(cov);
    gsl_multifit_linear_free(mw);

    throw std::runtime_error("Assertion failed: n != j");
  }

  double xStart = X.front();
  double xEnd =   X.back();

  /* use uniform breakpoints */
  gsl_bspline_knots_uniform(xStart, xEnd, bw);

  /* construct the fit matrix X */
  for (int i = 0; i < n; ++i)
  {
    double xi=gsl_vector_get(x, i);

    /* compute B_j(xi) for all j */
    gsl_bspline_eval(xi, B, bw);

    /* fill in row i of X */
    for (j = 0; j < ncoeffs; ++j)
    {
      double Bj = gsl_vector_get(B, j);
      gsl_matrix_set(Z, i, j, Bj);
    }
  }

  /* do the fit */
  gsl_multifit_wlinear(Z, w, y, c, cov, &chisq, mw);

  /* output the smoothed curve */
  API::MatrixWorkspace_sptr outWS = WorkspaceFactory::Instance().create(inWS,1,X.size(),Y.size());
  {
    outWS->getAxis(1)->setValue(0, inWS->getAxis(1)->spectraNo(spec));
    double xi, yi, yerr;
    for (MantidVec::size_type i=0;i<Y.size();i++)
    {
      xi = X[i];
      gsl_bspline_eval(xi, B, bw);
      gsl_multifit_linear_est(B, c, cov, &yi, &yerr);
      outWS->dataY(0)[i] = yi;
      outWS->dataE(0)[i] = yerr;
    }
    outWS->dataX(0) = X;
  }

  gsl_bspline_free(bw);
  gsl_vector_free(B);
  gsl_vector_free(x);
  gsl_vector_free(y);
  gsl_matrix_free(Z);
  gsl_vector_free(c);
  gsl_vector_free(w);
  gsl_matrix_free(cov);
  gsl_multifit_linear_free(mw);

  setProperty("OutputWorkspace",outWS);

}
Ejemplo n.º 2
0
/**
 * Execute smoothing of a single spectrum.
 * @param inputWS :: A workspace to pick a spectrum from.
 * @param wsIndex :: An index of a spectrum to smooth.
 * @return :: A single-spectrum workspace with the smoothed data.
 */
API::MatrixWorkspace_sptr
WienerSmooth::smoothSingleSpectrum(API::MatrixWorkspace_sptr inputWS,
                                   size_t wsIndex) {
  size_t dataSize = inputWS->blocksize();

  // it won't work for very small workspaces
  if (dataSize < 4) {
    g_log.debug() << "No smoothing, spectrum copied." << std::endl;
    return copyInput(inputWS, wsIndex);
  }

  // Due to the way RealFFT works the input should be even-sized
  const bool isOddSize = dataSize % 2 != 0;
  if (isOddSize) {
    // add a fake value to the end to make size even
    inputWS = copyInput(inputWS, wsIndex);
    wsIndex = 0;
    auto &X = inputWS->dataX(wsIndex);
    auto &Y = inputWS->dataY(wsIndex);
    auto &E = inputWS->dataE(wsIndex);
    double dx = X[dataSize - 1] - X[dataSize - 2];
    X.push_back(X.back() + dx);
    Y.push_back(Y.back());
    E.push_back(E.back());
  }

  // the input vectors
  auto &X = inputWS->readX(wsIndex);
  auto &Y = inputWS->readY(wsIndex);
  auto &E = inputWS->readE(wsIndex);

  // Digital fourier transform works best for data oscillating around 0.
  // Fit a spline with a small number of break points to the data.
  // Make sure that the spline passes through the first and the last points
  // of the data.
  // The fitted spline will be subtracted from the data and the difference
  // will be smoothed with the Wiener filter. After that the spline will be
  // added to the smoothed data to produce the output.

  // number of spline break points, must be smaller than the data size but
  // between 2 and 10
  size_t nbreak = 10;
  if (nbreak * 3 > dataSize)
    nbreak = dataSize / 3;

  // NB. The spline mustn't fit too well to the data. If it does smoothing
  // doesn't happen.
  // TODO: it's possible that the spline is unnecessary and a simple linear
  // function will
  //       do a better job.

  g_log.debug() << "Spline break points " << nbreak << std::endl;

  // define the spline
  API::IFunction_sptr spline =
      API::FunctionFactory::Instance().createFunction("BSpline");
  auto xInterval = getStartEnd(X, inputWS->isHistogramData());
  spline->setAttributeValue("StartX", xInterval.first);
  spline->setAttributeValue("EndX", xInterval.second);
  spline->setAttributeValue("NBreak", static_cast<int>(nbreak));
  // fix the first and last parameters to the first and last data values
  spline->setParameter(0, Y.front());
  spline->fix(0);
  size_t lastParamIndex = spline->nParams() - 1;
  spline->setParameter(lastParamIndex, Y.back());
  spline->fix(lastParamIndex);

  // fit the spline to the data
  auto fit = createChildAlgorithm("Fit");
  fit->initialize();
  fit->setProperty("Function", spline);
  fit->setProperty("InputWorkspace", inputWS);
  fit->setProperty("WorkspaceIndex", static_cast<int>(wsIndex));
  fit->setProperty("CreateOutput", true);
  fit->execute();

  // get the fit output workspace; spectrum 2 contains the difference that is to
  // be smoothed
  API::MatrixWorkspace_sptr fitOut = fit->getProperty("OutputWorkspace");

  // Fourier transform the difference spectrum
  auto fourier = createChildAlgorithm("RealFFT");
  fourier->initialize();
  fourier->setProperty("InputWorkspace", fitOut);
  fourier->setProperty("WorkspaceIndex", 2);
  // we don't require bin linearity as we don't need the exact transform
  fourier->setProperty("IgnoreXBins", true);
  fourier->execute();

  API::MatrixWorkspace_sptr fourierOut =
      fourier->getProperty("OutputWorkspace");

  // spectrum 2 of the transformed workspace has the transform modulus which is
  // a square
  // root of the power spectrum
  auto &powerSpec = fourierOut->dataY(2);
  // convert the modulus to power spectrum wich is the base of the Wiener filter
  std::transform(powerSpec.begin(), powerSpec.end(), powerSpec.begin(),
                 PowerSpectrum());

  // estimate power spectrum's noise as the average of its high frequency half
  size_t n2 = powerSpec.size();
  double noise =
      std::accumulate(powerSpec.begin() + n2 / 2, powerSpec.end(), 0.0);
  noise /= static_cast<double>(n2);

  // index of the maximum element in powerSpec
  const size_t imax = static_cast<size_t>(std::distance(
      powerSpec.begin(), std::max_element(powerSpec.begin(), powerSpec.end())));

  if (noise == 0.0) {
    noise = powerSpec[imax] / guessSignalToNoiseRatio;
  }

  g_log.debug() << "Maximum signal " << powerSpec[imax] << std::endl;
  g_log.debug() << "Noise          " << noise << std::endl;

  // storage for the Wiener filter, initialized with 0.0's
  std::vector<double> wf(n2);

  // The filter consists of two parts:
  //   1) low frequency region, from 0 until the power spectrum falls to the
  //   noise level, filter is calculated
  //      from the power spectrum
  //   2) high frequency noisy region, filter is a smooth function of frequency
  //   decreasing to 0

  // the following code is an adaptation of a fortran routine
  // noise starting index
  size_t i0 = 0;
  // intermediate variables
  double xx = 0.0;
  double xy = 0.0;
  double ym = 0.0;
  // low frequency filter values: the higher the power spectrum the closer the
  // filter to 1.0
  for (size_t i = 0; i < n2; ++i) {
    double cd1 = powerSpec[i] / noise;
    if (cd1 < 1.0 && i > imax) {
      i0 = i;
      break;
    }
    double cd2 = log(cd1);
    wf[i] = cd1 / (1.0 + cd1);
    double j = static_cast<double>(i + 1);
    xx += j * j;
    xy += j * cd2;
    ym += cd2;
  }

  // i0 should always be > 0 but in case something goes wrong make a check
  if (i0 > 0) {
    g_log.debug() << "Noise start index " << i0 << std::endl;

    // high frequency filter values: smooth decreasing function
    double ri0f = static_cast<double>(i0 + 1);
    double xm = (1.0 + ri0f) / 2;
    ym /= ri0f;
    double a1 = (xy - ri0f * xm * ym) / (xx - ri0f * xm * xm);
    double b1 = ym - a1 * xm;

    g_log.debug() << "(a1,b1) = (" << a1 << ',' << b1 << ')' << std::endl;

    const double dblev = -20.0;
    // cut-off index
    double ri1 = floor((dblev / 4 - b1) / a1);
    if (ri1 < static_cast<double>(i0)) {
      g_log.warning() << "Failed to build Wiener filter: no smoothing."
                      << std::endl;
      ri1 = static_cast<double>(i0);
    }
    size_t i1 = static_cast<size_t>(ri1);
    if (i1 > n2)
      i1 = n2;
    for (size_t i = i0; i < i1; ++i) {
      double s = exp(a1 * static_cast<double>(i + 1) + b1);
      wf[i] = s / (1.0 + s);
    }
    // wf[i] for i1 <= i < n2 are 0.0

    g_log.debug() << "Cut-off index " << i1 << std::endl;
  } else {
    g_log.warning() << "Power spectrum has an unexpected shape: no smoothing"
                    << std::endl;
    return copyInput(inputWS, wsIndex);
  }

  // multiply the fourier transform by the filter
  auto &re = fourierOut->dataY(0);
  auto &im = fourierOut->dataY(1);

  std::transform(re.begin(), re.end(), wf.begin(), re.begin(),
                 std::multiplies<double>());
  std::transform(im.begin(), im.end(), wf.begin(), im.begin(),
                 std::multiplies<double>());

  // inverse fourier transform
  fourier = createChildAlgorithm("RealFFT");
  fourier->initialize();
  fourier->setProperty("InputWorkspace", fourierOut);
  fourier->setProperty("IgnoreXBins", true);
  fourier->setPropertyValue("Transform", "Backward");
  fourier->execute();

  API::MatrixWorkspace_sptr out = fourier->getProperty("OutputWorkspace");
  auto &background = fitOut->readY(1);
  auto &y = out->dataY(0);

  if (y.size() != background.size()) {
    throw std::logic_error("Logic error: inconsistent arrays");
  }

  // add the spline "background" to the smoothed data
  std::transform(y.begin(), y.end(), background.begin(), y.begin(),
                 std::plus<double>());

  // copy the x-values and errors from the original spectrum
  // remove the last values for odd-sized inputs
  if (isOddSize) {
    out->dataX(0).assign(X.begin(), X.end() - 1);
    out->dataE(0).assign(E.begin(), E.end() - 1);
    out->dataY(0).resize(Y.size() - 1);
  } else {
    out->setX(0, X);
    out->dataE(0).assign(E.begin(), E.end());
  }

  return out;
}